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Question
Find the least number which when divided by 16, 36 and 40 leaves 5 as remainder in each case.
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Solution
On subtracting 5 from each number:
16 − 5 = 11
36 − 5 = 31
40 − 5 = 35
The required number will be the least common multiple of 11, 31 and 35.
L.C.M. of 11, 31 and 35 = 11×31×35 as they are relative prime numbers
= 11935
This is because they do not have any factor in common.
So, 11935 is the required number.
On subtracting 5 from each number:
16 − 5 = 11
36 − 5 = 31
40 − 5 = 35
The required number will be the least common multiple of 11, 31 and 35.
L.C.M. of 11, 31 and 35 = 11×31×35 as they are relative prime numbers
= 11935
This is because they do not have any factor in common.
So, 11935 is the required number.
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